As a solid tumor evolves, compressive stresses accumulate within the tumor due to growth. These stresses play important roles on tumor cells phenotype differentiation and tumor microenvironment conditions. Many mathematical models have been developed to represent tumor growth under deformation. From a continuum mechanics point of view, they are usually built by performing a kinematic decomposition, applying the momentum balance equation, and adding constitutive relations. This framework involves a series of assumptions that ultimately impact the prediction of the tumor deformation. A different framework can be pursued by using in vivo data to recover the tumor deformation. Here we investigate the use of a classical optical flow methodology known as the Lucas-Kanade technique to track tumor deformation in a synthetic experimental breast cancer setting. We also perform a model-free sensitivity analysis to study the impact of parameter uncertainties on the tumor evolution in the proposed modeling framework. We focus on the identification of the set of influential parameters with respect to the tumor area evolution, recognized as a meaningful quantity of interest. We show that optical flow techniques may capture deformations appearing in breast cancers, being a useful alternative to integrate in vivo deformation data to mathematical tumor models.

3D culture methods, by incorporating significant properties of cellular habitat, such as heterogeneous microenvironment, complex interactions of cells with their neighbor cells as well as local extracellular matrix, and complicated diffusion processes of nutrients and oxygen, provide a closer prediction of the real system. One of the most recent 3D biofabrication methods is 3D bioprinting which has contributed dramatically to the development of three-dimensionality and heterogeneity of the tumor microenvironment adequately to replicate characteristics of cancer tumor in vivo. Although 3D bioprinting is rapidly progressing in cancer-related studies, there is still a need to gain a better insight into cell growth mechanism post printing. Computational tools, such as cellular Automata Modelling can be a good complement to the In-vitro experiments that assists to simulate the breast cancer cells activity and growth while cells are encapsulated within porous hydrogel-based construct fabricated using extrusion-based 3D bioprinting technique.

The tip-over hypothesis of DNA damage therapy sensitivity proposes that cytotoxic therapy is effective if it pushes a cancer cell's somatic copy number alteration (SCNA) load above a tipping point. We present evidence that the tipping point is accounted for not by elevated SCNA load alone, but by an inability of the tissue micro-environment (TME) to provide the necessary resources. The energetic costs of DNA content levels required for high SCNA loads do not, in the absence of cytotoxic therapy, justify the masking benefits they bring. We investigate Oxygen, Phosphate and Glucose as candidate rate-limiting substrates of dNTP synthesis of cancer cells with variable DNA contents. Hereby we focus on stomach and brain tumors as two representative cancer types whose TME can “afford” different amounts of DNA. Our results point to the potential of tumor cell DNA content and dNTP substrate availability to predict a tumor's vulnerability to increasing SCNA rate.

Multiple myeloma is a largely incurable cancer characterized by the expansion of plasma cells in the bone marrow. Osteolytic lesions occur as a result of a “vicious cycle” between myeloma cells and trabecular bone that tips the balance of normal bone remodeling in favor of bone resorption. Standard of care treatments include bisphosphonates to slow down bone loss, and bortezomib, an anticancer therapy. Understanding how the composition of the bone microenvironment impacts the success of treatments using in vitro and in vivo methods alone remains a challenge. However, integration of biology and computational modeling allows a unique insight into the spatiotemporal aspects of myeloma progression and how treatments impact the disease.To explore these dynamics, we developed a hybrid agent-based model that incorporates key cell types that drive normal bone remodeling, including osteoclasts and osteoblasts, and use published data as well as our own to calibrate parameters such as the dose-dependent responses of treatments on myeloma and bone cells. We simulate the progression of myeloma growth and bone disease, starting from bone homeostasis, and explore how the “vicious cycle” is modified in the presence of treatments. This computational model has the potential to provide insight into better treatment strategies.

Prion proteins are associated with fatal neurodegenerative diseases in mammals, but they are also responsible for a number of harmless heritable phenotypes in yeast. Under certain experimental conditions, changes in protein aggregation dynamics between neighboring cells result in sectored colonies corresponding to loss of the prion phenotype. The resulting phenotypic organization provides a rich data set that can be used to uncover the non-intuitive relationships between protein aggregation mechanisms across multiple scales. In this talk, we introduce a novel, two-dimensional agent-based model of a budding yeast colony with detailed representation of cell-type specific biological processes, including budding, variation in cell-cycle length, and asymmetric protein segregation. The model is used to study the impact of budding cell division, nutrient limitation and yeast colony organization on yeast colony phenotypes. In the model, prion dynamics are simulated within each individual cell using simplified intracellular dynamics, and spatial arrangement of cells is modeled using a center-based modeling approach. The multiscale model may have the potential to predict mechanisms underlying experimentally observed phenomena such as sectored prion phenotypes in yeast colonies and serve as a tool for future hypothesis generation and testing.

Red blood cells are one of the most important components of life in humans. Loss of red blood cells has consequences, such as anemia or even death. Such a loss could be the result of parasitemia, viral infection, or phlebotomy. Red blood cell dynamics within a human involve several stages of precursor cells before a red blood cell fully matures to an erythrocyte. After blood loss, a feedback mechanism contingent on loss and level of erythrocytes causes the production of more precursor cells to return the blood dynamics to equilibrium. We seek to understand these dynamics from a biological perspective by using mathematics to model specific loss scenarios. We model this process using a system of nonlinear, deterministic, ordinary differential equations. Functions describing this feedback, the stem cell recruitment, and the erythrocyte loss are chosen to examine the system dynamics. Some parameter choices cause a Hopf bifurcation, while others lead to death, stable steady states, or limit cycles. Numerical methods are used to display bifurcation diagrams and transient dynamics. By understanding red blood cell dynamics through the utilization of mathematical modeling and dynamical systems tools, diseases can be mitigated as we understand the scenarios in which they occur.

Sprouting angiogenesis is the process by which new blood vessels grow from preexisting ones. It is a fundamental process during embryo development, as well as in many physiological (vascular remodeling, wound healing) and pathological phenomena (solid tumor growth, diabetic retinopathy). Angiogenesis is heavily dependent on a number of factors such as: the concentration of oxygen in the surrounding tissues, chemical signaling and endothelial cell coordination and proliferation. Cell migration is key for sprouting angiogenesis to occur since the new sprouts need to reach the cells in hypoxia. Thus, studying the forces exerted by cells on the extracellular matrix (ECM) and how the matrix's mechanical properties affect cell migration can help us understand the role angiogenesis plays in different processes.We have developed a mathematical model using the phase field method taking into account the elastic interactions between endothelial tissue and ECM, as well as the adhesion and traction forces exerted by cells. At the same time, we have used in vitro, aortic ring assays using mouse aorta slicesto quantify the cell's migration potential in gels with different rigidities.Both studies show that there is a value of ECM rigidity that results in an optimal migration distance.

We present a combined in silico / in vitro approach to optimising experimental muscle cell culturing protocols using an agent-based model (ABM). Functions of experimentally derived and inferred cell behaviours are applied as inputs and levels of myocyte-myotube fusion, an indicator of experimental success, as an output. We conducted sets of in vitro experiments to obtain fixed and time-lapse images of myocyte differentiation and myotube maturation under a range of media serum concentrations and concentrations of N2B27 neuron differentiation medium. Metrics of myoblast motion and proliferation were quantified from time-lapse imaging and used to inform a cell residence-time dependent ABM of myoblast-myotube fusion. An Approximate Bayesian Computation method was applied to infer the myocyte residence-time threshold by comparing ABM simulations with cell fusion data extrapolated from stained images.Once validated, the ABM was used to run in silico experiments over a range of media conditions to predict the conditions most likely to produce quality muscle tissue. A sweep of the behavioural parameters defining the ABM was conducted to assess the relative effect size of individual cell behaviours on cell fusion.We also discuss extending the protocol to analyse the spatial distribution of nuclei as a quality indicator.

Many biological populations reside in increasingly fragmented landscapes, which arise from human activities and natural causes. Landscape characteristics may change abruptly in space and create sharp transitions (interfaces) in landscape quality. We study how interactions between individuals and populations in a predator-prey system are affected by habitat fragmentation.We model population dynamics with a predator-prey system in a coupled ecological reaction-diffusion equation in a homogeneous landscape to study Turing patterns that emerge from diffusion driven instability (DDI). We derive the DDI conditions and then we use a finite difference scheme method to numerically explore the general conditions using the May model and we present numerical simulations to illustrate our results. Then we extend our studies on Turing pattern formation by considering a predator-prey system on an infinite patchy periodic landscape. The movement between patches is incorporated into the interface conditions that link the reaction-diffusion system between patches. We use a homogenization technique to obtain an analytically tractable approximate model and determine Turing pattern formation conditions. We use numerical simulation to present our results from this approximation method for this model to explore how differential movement and habitat preference of both species in this model, prey and predator, affect DDI.

The importance of habitat heterogeneity on a diffusing population is crucial to understand population dynamics. In this talk, we formulate a reaction-diffusion population model to study the effect of resource allocation in an ecosystem with resources having their own dynamics in space and time. This approach is more realistic than simply assuming the resource level is not changing as the population changes. Furthermore, we solve an optimal control problem of our ecosystem model to maximize the abundance of a single species while minimizing the cost of inflow resource allocation.

The augmentation of natural enemies against agricultural pests is a common tactic undertaken to minimize crop damage without the use of chemical pesticides. Failures of this strategy may result from (i) Allee effects acting on biological control agent; (ii) trophic interactions between the released control agent and native species in the local ecosystem; (iii) excessively rapid spreading agents. To investigate the interplay of these mechanisms in pest biocontrol efficiency in the context of intraguild predation (IGP), we develop a one-dimensional dynamical model of a spatial, tritrophic food web with intraguild predation. We show that the agent's diffusivity (i.e., agent's dispersal speed), and intraguild predator's addition of alternative food sources are important factors in determining the success or failure of pest biocontrol. These results are obtained for spatially explicit models by considering the speed of dispersal of the control agent and the pest. Feedback from theoretical models as the one constructed in this work can provide useful guidelines for practitioners in biological control.

Cyclic and oscillatory behaviors are ubiquitous in ecological systems. These oscillations can be noise-induced or due to intrinsic ecological interactions. Due to the stochastic nature of ecological systems, these types of oscillations appear to be very similar and distinguishing between them using ecological data is a topic of active research. Intrinsic oscillations, unlike noise-induced oscillations, are known to be readily synchronized by local coupling. We propose that spatial patterns in spatially extended systems may contain indirect information about whether cycles are noise-induced or intrinsic. We explore this idea using an ecological model with a period-doubling route to chaos, comparing noise-induced cycles in the stable regime to intrinsic oscillations in the 2-cycle regime, on a lattice with nearest neighbor coupling. Such models implemented on the lattice undergoes a second order phase transition from disordered to synchrony. Our results show that although noise-induced and intrinsic oscillations are effectively indistinguishable in the disordered state, the onset of synchrony allows us to differentiate between these two causes of cycles, across a range of spatial scales of observation.

The structure of plant roots has a large impact on the environment through ground nutrient usage and underground carbon fixation. Crop plants can be improved to reduce fertilizer usage and combat climate change through identification of the genes controlling root structural traits. However, this remains challenging due to the highly variable and responsive nature of root growth. I derive new traits using characteristics of matrices and multivariate normal distributions (MVN) of roots from a diversity panel. The Sorghum diversity panel consists of 600 unique genotypes from around the world. The genotypes were grown in controlled conditions and X-ray imaged. From these images I obtain square matrices of root locations as a function of depth. The matrices are then analyzed and MVN distributions estimated to obtain root distribution information of each Z-slice. The resulting features include entropy, eccentricity, and the two largest eigenvalues of the covariance matrix. The ability of these characteristics to measure root structural traits are benchmarked against existing highly heritable traits, such as root depth and mass. Finally, after applying dimension reduction techniques, we can identify significant changes over depth and the genetic loci controlling highly heritable structural traits.

We investigate the role of landscape structure on a range expansion with mutation and selection, using a generalised Eden model. In this lattice model, sites are occupied by wild type or mutant, or empty until infected by a neighbouring site. A phase transition between long-term mutant domination of the population front and coexistence has been characterised in a homogeneous environment for slower-growing mutants in the absence of back mutations [Kuhr et al., NJP, 2011].We here investigate the effect of randomly distributed circular patches that can only be invaded by the mutant - reminiscent of pesticide-treated areas that can only be invaded by resistant pests. Our simulations show that at surprisingly low patch density, mutants can dominate even at fitness lower than which is required in a homogeneous environment. Patches bestow a spatial advantage upon the mutants, enlarging mutant domains that can then overlap with downstream patches, leading to a cascade of patch to patch infection by the mutant domain. This argument can be quantified by combining geometrical arguments for domain boundaries with percolation theory.Our results provide an indication for the long-term dynamics of an expanding population frontier in an inhomogeneous medium, under the effects of mutation and selection.

When parameterizing dynamical systems models of biological processes, we often use summary statistics (e.g., the mean) reported in experimental or observational studies. However, these summary statistics are abstractions, concealing variation occurring over space, time, or among individuals. Further, we know that the behavior of a nonlinear model using mean parameter values will differ from the mean model behavior if the parameter is instead treated as a random variable. Algae growing within polar sea ice provides an example of a system where extreme local heterogeneity in environmental conditions results in local heterogeneity in algal growth rates. Ignoring this and using a fixed, mean growth parameter to approximate regional dynamics can result in incorrect predictions of bloom timing and magnitude. Instead, algal growth rates at a given location should be treated as a random variable capturing the known heterogeneity. In this talk, I will provide an introduction to generalized polynomial chaos as an elegant, computationally efficient method for incorporating heterogeneous growth rates into standard algal bloom models, resulting in improved predictions of bloom dynamics. This method is broadly applicable for any system where local heterogeneity needs to be accounted for when considering aggregate dynamics over larger scales.

In human social systems, it is natural to assume that individuals' opinions influence and are influenced by their interactions. Mathematically, it is common to represent such systems as networks, where nodes are individuals and edges between them denote a connection. Adaptive network models explore the dynamic relationship between node properties and network topology. In the context of opinion dynamics, these models often take the form of adaptive voter models, where there are two mechanisms through which network changes can take place. Through homophily, an edge forms between two individuals who already agree. Through social learning, an individual adopts a neighbor's opinion. In these models, individuals are more frequently attached to those who share their opinion, seen through the formation of sub-communities of like-minded individuals. However, it is not always the case that individuals want to cluster into homogeneous groups. Instead, they might attempt to surround themselves with those who both agree and disagree with them to attain a balance of inclusion and distinctiveness in their social environments. In this work, we explore the effects that such heterogeneous preferences have on the dynamics of the adaptive voter model.

In Brazil, school closure was one of the first interventions adopted to contain the spread of Sars-Cov-2. While maintaining this intervention for an extended period presents increasing social costs, there is a reasonable concern regarding the epidemiological consequences of reopening schools during the pandemic. Here, we model the epidemiological dynamics in scenarios of school reopening for 3 capitals of Brazil, and how mitigation measures such as contact tracing can contribute to reduce the risk of transmissions. We implement an extended SEIR model stratified by age and contact networks at different environments (school, home, work, and others), and the transmission rate is affected by distinct intervention measures. After fitting epidemiological and demographic data, we simulate scenarios of increasing school transmission due to school reopening. The effects of contact tracing strategies in reducing transmission in school contacts are explored. Our results indicate that a flexibilization in the school closure intervention results in a non-linear increase of reported cases and deaths, that is dependent on the previous prevalence of cases in the population. Also, when contact tracing is restricted to school settings, a large number of daily tests are required to produce significant effects in reducing the total number of infections and deaths.

A gene drive is a genetic mechanism that can spread a gene through a population. Gene drives have the potential to significantly change the way we control vector-borne diseases, most notably dengue and malaria, with mathematical models having demonstrated their potential effectiveness. A key consideration absent from the mathematical modeling literature is the influence of density-dependence on target populations. Density-dependence is a natural ecological process that can counteract population suppression by a gene drive. The purpose here is then to study gene drive performance in a population of mosquitoes with density-dependent characteristics and determine how this affects infectious disease control. We use a mathematical framework in which a model for mosquito population genetics and dynamics is coupled to an epidemiological model. We explore a variety of different scenarios relating to the type of transgene released (e.g. varying sex-specific lethality). We undertake a sensitivity analysis to explore performance over a wide range of scenarios and to identify key parameters that influence the effectiveness of the approach. In each situation, results of system analysis with and without density-dependence is compared, and to what extent such factors influence certain quantities of interest such as disease prevalence in a human population.

Control strategies that employ real-time polymerase chain reaction (RT-PCR) tests for the diagnosis and surveillance of COVID-19 epidemic are inefficient in fighting the epidemic due to high cost, delays in obtaining results, and the need of specialized personnel and equipment for laboratory processing. Cheaper and faster alternatives have been proposed, which return results rapidly, but are less sensitive in detecting virus. To quantify the effects of the tradeoffs between sensitivity, cost, testing frequency, and delay in test return on the overall course of an outbreak, we built a multi-scale immuno-epidemiological model that connects the virus profile of infected individuals with transmission and testing at the population level. For fixed testing capacity, lower sensitivity tests with shorter return delays slightly flatten the daily incidence curve and delay the time to the peak daily incidence. However, compared with RT-PCR testing, they do not always reduce the cumulative case count at half a year into the outbreak. When testing frequency is increased to account for the lower cost of less sensitive tests, we observe a large reduction in cumulative case counts. We predict that surveillance testing that employs low-sensitivity tests at high frequency can be an effective tool for epidemic control.

Several vaccines with different efficacies are currently being distributed across the world to control COVID-19. Having enough doses from the most efficient vaccines in a short time is not possible for all countries. Hence, policy-makers may propose using various combinations of available vaccines to eliminate the disease quickly by achieving herd immunity. The classic herd-immunity threshold suggests that we can eliminate outbreaks from a population by vaccinating a fraction of the population. However, that classic threshold is for a single vaccine and is invalid and biased when we have multiple-vaccine strategies for a disease. Therefore, making decisions for vaccine-allocation policies based on this threshold may be costly. Here, we formulate the problem and find the exact threshold for the case with multiple-vaccine strategies for a single disease and show that there is more than one strategy to achieve herd immunity. Unlike the single-vaccine case, herd immunity can be achieved with an unlimited number of vaccine-allocation policies when multiple vaccines are available. Moreover, we propose methods to find the optimal strategy in a set of multiple-vaccination strategies.

In network control theory, driving all the nodes in the Feedback Vertex Set (FVS) forces the network into one of its attractors (long-term dynamic behaviors), but the FVS is often composed of more nodes than can be realistically manipulated in a system (e.g., 1-3 nodes for intracellular networks). Thus, we developed a method to identify subsets of the FVS on Boolean models of intracellular networks using topological, dynamics-independent measures. We identified seven topological measures sorted into three categories — centrality measures, propagation measures, and cycle-based measures. Each measure was ranked and then evaluated against two dynamics-based metrics that measure ability of interventions to drive the system towards or away from their attractors: To Control and Away Control. After examining various biological networks, we found that the FVS subsets that ranked highest according to the propagation metrics could most effectively control the network. This result was independently corroborated on an array of different Boolean models of biological networks. Consequently, overriding the entire FVS is not required to drive a biological network to one of its attractors, and this method provides a way to reliably identify these FVS subsets without knowledge of the network's dynamics.

A fundamental problem in mathematical modeling is the determination of model parameter values from experimental data. In disease and immunological studies, repeated collection of data from a single subject is impossible, because the disease or the manipulations performed in the experiments are fatal to the subject, or permanently alter the subject's immune system. Therefore, parameter identification or estimation of nonlinear ODE systems from a single trajectory has been studied in my research. Many computational techniques for parameter estimation has been employed. However, it is also important to have rigorous, theoretical results, addressing the questions whether there exists solution, a unique solution, or no solution to the parameter estimation problem. If we view the models as forward mappings from parameter values to states of model variables, then the parameter identification/estimation from data can be formulated as the problem of inverting this mapping. Therefore this is an inverse problem and its solution is the set of parameters values. In particular, in my research, I focus on a certain type of nonlinear systems, which is linear-in-parameters system. I will use the two-dimensional Lotka-Volterra system as an example to show our results and explain difficulties in this research area.

During hemostasis in wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. Activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We present a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin and intermediate complexes. A tailored parameter subset selection technique is implemented to evaluate parameter identifiability for a representative dataset for fibrin accumulation. Our approach is based on systematic analysis of the eigenvalues and eigenvectors of the information matrix for the quantity of interest fibrin matrix via optimization, based on a least squares objective function. Capabilities of this approach to decrease the objective cost and integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability and aid in model reduction are also demonstrated. These findings illustrate the high degree of information within a single fibrin accumulation curve using a tailored model and parameter subset selection approach that can improve optimization and reduce model complexity.

In certain biological systems, such as the plumage pattern of birds and stripes on certain species of fishes, pattern formation take place behind a wave of competency. For these systems, one needs to consider the patterns that form when a particular type of growth -- apical growth -- is included. In this study, we use a particular type of partial differential equation model, known as a Turing diffusion-driven instability model, to study pattern formation on apically growing domains, under a variety of rates of growth. Numerical simulations show that in one spatial dimension a slower growth rate drives a sequence of peak splittings in the pattern, whereas a higher growth rate leads to peak insertions. In two spatial dimensions, we observe stripes that are either perpendicular or parallel to the moving boundary under slow or fast growth rates, respectively. To understand this phenomenon, we use stability and bifurcation analysis to understand the process of selection of stripes or spots. Finally, we argue that there is a correspondence between the one- and two-dimensional phenomena, and that apical growth can account for the pattern organization observed in many biological systems.

When analyzing neuron models, ODE(Ordinary Differential Equation)-based models are used to study the characteristics of neurons and in turn understand the various complexities of neurons and their relations with abnormalities and hazards. But the biggest challenge of ODE-based models are its computational complexities and hence researchers started focusing on less complex models resulting in discrete models of neurons. A neuron exhibits bursting and spiking behavior depending on the resetting process which happens in every iteration step. In ODE models this iteration step decides the accuracy of the neuron models while in discrete models the iteration step is one and hence the accuracy is not affected. In this talk, I am going to introduce the discrete Izhikevich model which is modified version of the well-known ODE based Izhikevich neuron model. I analyze the complete dynamical properties and bifurcation patterns of the discretised model. It is found that a careful application of electric field on embryonic neuronal cells have led to their growth in cultures. Therefore, it is of interest to consider the effect of external electromagnetic field on the dynamical behavior of the neurons. I will show how the dynamics changes when external electromagnetic field is applied.

Located in hypothalamus, the gonadotropin-releasing hormone (GNRH) neurons trigger the reproductive axis by the synchronized release of gonadotropin-releasing hormone. The action potential propagating along the neuron's membrane activates the voltage-gated calcium channels, and the influx of the extracellular calcium activates the internal calcium stores. The resulting increase of the calcium ion concentration is crucial for the hormone exocytosis. The existing models of this phenomenon successfully explain the calcium transients along the dendrite of the GnRH neuron. However, the latest experimental results show a dramatic increase in the amplitude of the calcium concentration transients with the propagation along the dendrite. We conjecture that this amplitude increase is, in fact, the main reason for the synchronized release of the GnRH hormone and offer a new model for the calcium dynamics. The computational results based on the suggested model correlate with the experimental data.

This talk focuses on the Hindmarsh-Rose neuron model in a chaotic regime, and we consider a mechanism by which the system enters into a periodic state when driven by a signal from a chain of neurons. Previous work in nonlinear dynamics has shown that chaotic systems may be driven into periodic states (called cupolets) when driven by instantaneous impulses, using information theoretic and graph theoretic methods. In related work studying a coupled two cell FitzHugh-Nagumo neural model, it was possible for the combined system to enter into chaotic behavior, and through interaction and neural learning, mutually stabilized periodic states could be achieved. However, cupolet states were not possible because of the low dimensionality of the individual neurons. Here, we show that the Hindmarsh-Rose model, in a chaotic regime, may exhibit stabilized cupolets when impulses are applied on two Poincare surfaces. We report on several interesting properties of the cupolets. We then show how certain interactions between cupolets lead to chaotic stabilization in neural systems, with examples including a bidirectional neural system, a chain of neurons, and a feedback network. We conclude with a discussion of the implications and future directions of this research.

This talk continues the presentation Mathematical Models for Living Forms in Medical Physics Submodel 1: The information processing from teeth to Nerves from the Biophysics Annual Meeting 2020 Conference and American Physical Society Conferences. In the Submodel 1 the information processing from teeth to the nerves is modeled. The information is passed via p-waves through the tooth layers enamel and dentin. Odontoblasts located in the liquid in the tubules of the tooth dentin layer perform finally the transformation into electrical information (an electrical signal) that passes along nerves. The Submodel 2 of the project is dedicated to the information coding of the information from an entity hitting/touching a tooth and to the information processing of the coded unit through the nerves. Emphasized are the information representation as an electrical code and the coded information flow in the living system.

Since roughly 90% of lung cancer deaths occur due to the presence of metastases and their resulting symptoms. Therefore the identification and evaluation of metastases is of utter importance for optimal treatment. Modern imaging technology leaves most metastases undiscovered as their size is too small to be recognised. Nonetheless, they play an important role in therapy success. We quantified the metastatic size distribution in cancer patients and estimated the effects of possible different treatment applications. The framework presented is a coupled ODE/PDE model based on a McKendrick-von-Foerster equation introduced by Iwata et al. and modified along its characteristics to account for therapeutic effects in treatment applications. The continuous definition also allows to model the metastatic cascade, thus the transition of a single primary tumor to a metastatic disease. These simulations could help clinicians to compare outcomes and to choose among treatment possibilities based on different therapy goals. Retrospective analysis with clinical data allows for follow-up prognostic possibilities that will be shown in this presentation.

IntroductionThere is a need to discover better treatment strategies for patients with advanced head and neck squamous cell carcinoma (HNSCC). 45 patients with advanced HNSCC were treated with combination cetuximab (anti-EGFR) and nivolumab (anti-PD-1) every 2 weeks with a 2-week lead-in of cetuximab alone in a phase I/II clinical trial. However, not every patient responded to the protocol therapy. Therefore, there is a clinical need to identify high-risk patients. MethodsAvailable patient-specific information includes CT-derived sum of longest diameters every 8 weeks. We train a tumor growth inhibition (TGI) ODE model describing a uniform growth rate and initial treatment sensitivity and patient-specific rate of evolution of resistance. We forecast tumor burden and predict risk level at the second and third observations.ResultsThe TGI model is able to accurately represent tumor burden dynamics (R2=0.98). However, forecasts for tumor burden are rather poor. However, since our main concern is predicting risk level, we continue with the study and achieve decent predictions at second and third observations (n=25,14 patients, accuracy=0.64,0.71, respectively).ConclusionGiven enough on-treatment information, a clinician can use the TGI model to predict high-risk patients on the trial protocol.

PARP inhibitors (PARPis) represent a great advancement in the treatment of ovarian cancer, yet these drugs still often fail after a few months due to emerging drug resistance. A recent clinical trial in prostate cancer showed that evolutionary-inspired, adaptive drug scheduling significantly delayed time to progression. This approach modulated treatment to maintain a pool of drug-sensitive cells that suppress resistant cells through competition. Here, we present results from a combined modelling and experimental study in which we investigated whether adaptive therapy can delay resistance to the PARPi Olaparib. We performed a series of in vitro experiments in which we used time-lapse microscopy to characterise the cell population dynamics under different PARPi schedules. Our work reveals a delay in drug response, and that cells recover quickly upon drug withdrawal. Thus, treatment interruptions or modulations need to be carefully timed. To explain this behaviour we develop an ODE model which attributes the dynamics to the fact that PARPis induce cell cycle arrest from which cells may still recover. This model can not only fit the in vitro data, but it also accurately predicts the response to unseen drug schedules. We conclude with in silico trials of a plausible adaptive PARPi strategy.

In 1972 H. P. Greenspan proposed one of the first mathematical models to describe avascular tumour spheroid growth. He suggested that his work be experimentally validated when improved technology was available. Remarkably, even though his paper has been highly influential and well-cited it has not yet been experimentally validated. In this presentation we will directly connect the Greenspan model to experimental data for the first time. Using live-dead cell staining and fluorescent ubiquitination-based cell cycle indicator (FUCCI) technology, we reveal and measure necrotic, quiescent, and proliferative regions inside growing tumour spheroids. These novel data, that we collect across a number of initial tumour spheroid sizes, cell lines, and experimental designs, allows us to test the Greenspan model and form confidence intervals for its parameters.